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Beta Assertive Graphs

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Diagrammatic Representation and Inference (Diagrams 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12169))

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Abstract

Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propositional AGs to Beta by lines. Absence of polarities necessitate Beta-AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.

The paper was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project ‘5–100’.

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Notes

  1. 1.

    Symbolizing two quantifiers separately derives from Peirce’s 1882 notation [2, 7].

  2. 2.

    Any line depicted on antecedent areas as loose may be continuous, branching or connected, just as ligatures may be in Beta-EGs.

References

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  2. Bellucci, F., Pietarinen, A.-V.: From Mitchell to Carus: fourteen years of logical graphs in the making. Trans Peirce Soc. 52, 539–575 (2016)

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  9. Pietarinen, A.-V., Chiffi, D.: Assertive and existential graphs: a comparison. In: Chapman, P., Stapleton, G., Moktefi, A., Perez-Kriz, S., Bellucci, F. (eds.) Diagrams 2018. LNCS (LNAI), vol. 10871, pp. 565–581. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91376-6_51

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Author information

Authors and Affiliations

  1. University of Bologna, Bologna, Italy

    Francesco Bellucci

  2. Politecnico di Milano, Milan, Italy

    Daniele Chiffi

  3. Tallinn University of Technology, Tallinn, Estonia

    Ahti-Veikko Pietarinen

  4. HSE University, Moscow, Russia

    Ahti-Veikko Pietarinen

Authors
  1. Francesco Bellucci
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  2. Daniele Chiffi
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  3. Ahti-Veikko Pietarinen
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Corresponding author

Correspondence to Ahti-Veikko Pietarinen .

Editor information

Editors and Affiliations

  1. Tallinn University of Technology, Tallinn, Estonia

    Ahti-Veikko Pietarinen

  2. Edinburgh Napier University, Edinburgh, UK

    Peter Chapman

  3. University of Groningen, Groningen, The Netherlands

    Leonie Bosveld-de Smet

  4. Université de Lorraine, Nancy, France

    Valeria Giardino

  5. Columbia University, New York, NY, USA

    James Corter

  6. University of Liverpool, Liverpool, UK

    Sven Linker

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Bellucci, F., Chiffi, D., Pietarinen, AV. (2020). Beta Assertive Graphs. In: Pietarinen, AV., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds) Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science(), vol 12169. Springer, Cham. https://doi.org/10.1007/978-3-030-54249-8_49

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  • DOI: https://doi.org/10.1007/978-3-030-54249-8_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54248-1

  • Online ISBN: 978-3-030-54249-8

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